Emergent Symmetries in Quantum Field Theories

2023 Fiscal Year Final Research Report

• Project/Area Number: 19K03820
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 15010:Theoretical studies related to particle-, nuclear-, cosmic ray and astro-physics
• Research Institution: The University of Tokyo
• Principal Investigator: Yamazaki Masahito 東京大学, カブリ数物連携宇宙研究機構, 教授 (00726599)
• Project Period (FY): 2019-04-01 – 2024-03-31
• Keywords: 対称性の創発 / 超対称場の理論 / 位相的場の理論 / 頂点作用素代数 / 可積分系 / ホログラフィー / アンサンブル平均

Outline of Final Research Achievements

While more symmetries are broken as we lower the energy scale of the theory in most of the examples we know, it is known that there are some exceptional cases where symmetries emerge. In this research, we aimed for better understanding of emergence of symmetries by combination of physical and mathematical methods. More concretely, we started with examples of theories with emergent supersymmetries in the low energies (originally discovered by author and collaborators), and constructed topological quantum field theories by taking appropriate limits of the supersymmetric partition functions. We also discussed emergence of Yangian-type infinite-dimensional symmetries in the BPS sectors of supersymmetric field theories, and constructed for the first time examples where the proposed correspondence between integrable models and quantum field theories break down. We moreover discussed examples of emergent global symmetries in the discussion of ensemble averages in holography.

Free Research Field

素粒子理論

Academic Significance and Societal Importance of the Research Achievements

対称性が創発する現象自体は我々の世界の理解の根源に関わる極めて基礎的な問題である．本研究ではこの問いに対して，具体的な超対称場の理論を考え，さらに超対称局所化や可積分などの数理的手法を併用して迫り，結果として数理的構造である位相的場の理論のデータ（モジュラーテンソル圏）や可積分系（ヤンギアン）などを同定するに至った．さらにホログラフィーのアンサンブル平均において対称性が創発する現象も議論した．これらの成果は，物理学そのものについての根源的な問いと最先端のテクニックや数理を関係づける可能性を明示してみせたものであり，将来におけるさらなる研究のための雛形になるものであると考えている．